Projection of Line/Vector on a Plane

Projection of a Line having direction vector $$\vec{A}$$ on a plane having normal vector $$\vec{B}$$ is given by following formula

$$\vec{P}= (\frac{\vec{B} \times (\vec{A} \times \vec{B})}{\vert \vec{B} \vert ^2})$$

In the above formula $$\vec{P}$$ is the projected vector. Please note that this is same as vertical (perpendicular) projection of vector $$\vec{A}$$ on $$\vec{B}$$